Among 80 students, 24 passed in Chemistry, 35 passed in Physics and 29 passed in Mathematics, 8 students did not appear for the examination. If 2 students have passed in all the three subjects, 2 students have passed in Physics and Chemistry both but not in Mathematics, 2 students have passed in Chemistry and Mathematics both but not in Physics, and 8 students have passed in Physics and Mathematics both but not in Chemistry, then how many students have passed in Mathematics only?
Among 80 students, 24 passed in Chemistry, 35 passed in Physics and 29 passed in Mathematics, 8 students did not appear for the examination. If 2 students have passed in all the three subjects, 2 students have passed in Physics and Chemistry both but not in Mathematics, 2 students have passed in Chemistry and Mathematics both but not in Physics, and 8 students have passed in Physics and Mathematics both but not in Chemistry, then how many students have passed in Mathematics only? Correct Answer 17
This is a Venn diagram based question. According to the question,
Total no. of students = 80
Total no. of students passed in Chemistry = 24
Total no. of students passed in Physics = 35
Total no. of students passed in Mathematics = 29
No. of students who did not appear for the examination = 8 (say p)
No. of students who passed in all the three subjects = 2 (say x)
No. of students who passed in Physics and Chemistry both but not in Mathematics = 2 (say y)
No. of students who passed in Chemistry and Mathematics both but not in Physics = 2 (say z)
No. of students who passed in Physics and Mathematics both but not in Chemistry = 8 (say a)
Therefore,
No. of students who passed in Mathematics only = 29 - (x + z + a) = 29 - (2 + 2 + 8) = 17 (say d)
No. of students who passed in Chemistry only = 24 - (x + z + y) = 24 - (2 + 2 + 2) = 18 (say b)
No. of students who passed in Physics only = 35 - (x + y + a) = 35 - (2 + 2 + 8) = 23 (say c)
The logical Venn diagram is :
[ alt="F1 Archana Madhu 06.02.21 D1" src="//storage.googleapis.com/tb-img/production/21/02/F1_Archana_Madhu_06.02.21_D1.png" style="width: 390px; height: 235px;">
Hence, 17 is the correct answer.
